

A006157


a(n+1) = (n1) a(n) +n.n!.
(Formerly M3950)


4



1, 5, 28, 180, 1320, 10920, 100800, 1028160, 11491200, 139708800, 1836172800, 25945920000, 392302310400, 6320426112000, 108101081088000, 1956280854528000, 37347179950080000, 750144785854464000, 15813863053148160000, 349121438173347840000
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OFFSET

2,2


COMMENTS

Number of ascending runs of length at least two in all permutations of [n]. Example: a(3)=5 because we have (123), (13)2, 3(12), 2(13), (23)1 and 321, where the ascending runs of length at least 2 are shown between parentheses.  Emeric Deutsch and Ira M. Gessel, Sep 07 2004


REFERENCES

J. Francon, Histoires de fichiers, RAIRO Informatique Th\'{e}orique et Applications, 12 (1978), 4962.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

Table of n, a(n) for n=2..21.


FORMULA

(2n1)/6 * n!.
E.g.f. = x^2*(3x)/[6(1x)^2].  Emeric Deutsch and Ira M. Gessel, Sep 07 2004


MATHEMATICA

Table[(2n1)/6*n!, {n, 2, 30}] (* Harvey P. Dale, Jan 06 2014 *)


CROSSREFS

Cf. A014484.
Sequence in context: A082031 A020081 A095676 * A179326 A156629 A123776
Adjacent sequences: A006154 A006155 A006156 * A006158 A006159 A006160


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Simon Plouffe


EXTENSIONS

More terms from Harvey P. Dale, Jan 06 2014


STATUS

approved



